Shared genetic architecture between gastro-esophageal reflux disease, asthma, and allergic diseases

The aim is to investigate the evidence for shared genetic architecture between each of asthma, allergic rhinitis and eczema with gastro-esophageal reflux disease (GERD). Structural equation models (SEM) and polygenic risk score (PRS) analyses are applied to three Swedish twin cohorts (n = 46,582) and reveal a modest genetic correlation between GERD and asthma of 0.18 and bidirectional PRS and phenotypic associations ranging between OR 1.09-1.14 and no correlations for eczema and allergic rhinitis. Linkage disequilibrium score regression is applied to summary statistics of recently published GERD and asthma/allergic disease genome wide association studies and reveals a genetic correlation of 0.48 for asthma and GERD, and Genomic SEM supports a single latent factor. A gene-/gene-set analysis using MAGMA reveals six pleiotropic genes (two at 12q13.2) associated with asthma and GERD. This study provides evidence that there is a common genetic architecture unique to asthma and GERD that may explain comorbidity and requires further investigation.

Applying MiXeR to these summary statistics would also improve the depth of the analysis.
The analysis could benefit from downstream evaluation and discussion of vertical vs horizontal pleiotropy for the genes that are highlighted.
The results shown in Figure S11 should be discussed in the main text Minor points: "a number of intervention studies aiming to improve asthma symptoms by using antireflux (acid reducing) medication have not been successful" Have studies tested the effectiveness of using asthma medications to reduce GERD symptoms or in an in vitro/benchtop setting?
A more detailed description of the symptoms of GERD and the atopic traits (and the impact on affected patients quality of life) would help improve the motivation for this study.
A 6x6 heatmap showing the genetic correlations between all traits would be much more informative than what is shown in table 3.
The y-axis label should be fixed in Figure S1 Figure S10 seems to be missing data 1

Response to Communica ons Biology Reviewers 'Shared gene c architecture between gastro-esophageal reflux disease, asthma and allergic diseases: applica on of gene cally informa ve methods'.
Reviewer 1.
1.In the results sec on, many results are illustrated and presented with supplementary tables or figures.If these results are important, they should be in the main text rather than the supplement.
[Response] Thank you.We have now moved Table S1 describing the studies from which we used the summary sta s cs to the main text (new Table 1), and added a new figure, Figure 2, which highlights the new genomic SEM results, as suggested by reviewer #2 (see below).The remaining results are s ll presented in the supplement due to space limita ons and that they mostly focus on subgroup outcomes of secondary importance to the main findings.

Some data in the ar cle are not clearly explained.
A. "Polygenic associa ons were observed between asthma and GERD in the range of OR 1.09-1.14per one SD increase in PRS." in the abstract sec on, 1.09-1.14 is the result of which table?
[Response] These results come from Figure 1 and Supplementary Table 8.The adjusted odds ra os and 95% confidence intervals have now been added to Figure 1 so that they are in the main manuscript.
B. "Phenotypic associa ons were confirmed for: asthma and GERD-adjusted odds ra os (adjOR) 1.68, 95% CI 1.43, 1.98; allergic rhini s and GERD-adjOR 1.19 (95%CI 1.02, 1.39); eczema and GERD-adjOR 1.22 (95%CI 1.01, 1.47)." in the first paragraph of the results sec on, how are the results calculated and from which table ?[Response] Thank you.The phenotypic associa ons were es mated using generalized es ma ng equa on models as described in the sta s cal analyses sec on, first paragraph.We realized this was not presented in a separate table as part of this had been published previously (h ps://onlinelibrary.wiley.com/doi/full/10.1111/cea.14106).The bivariate associa ons between asthma/allergic traits and GERD are now tabulated in Table S2 in the supplementary materials: Table S2.Bivariate associations between asthma/allergic traits and GERD.[Response] Our reading of the results sec on paragraph 2 and Table 2 is that they are the same.The results for asthma and allergic rhini s are read from the AE model in the table.However, in line with the reviewers broader concern, we have checked through the manuscript for all values presented in the main text to align with the tables/figures.

Reviewer #2:
The authors provide a cross-trait analysis to measure the gene c component of the shared e ology between GERD and atopic diseases.While long known to be clinically correlated, this represents an important step to understanding the gene cs of these complex traits and narrow in on biology.
Major points: 1.The introduc on would benefit from a summary of the literature describing the heritability of these traits (both twin-based es mates and SNP-based es mates).Further discussion of the complex gene cs and the complex environmental risk factors would help frame the ques on of focus.How much of the of the variance in these phenotypes has been explained through the latest PRS approaches? [Response] Arehart CH et al, JACI 2022).Unfortunately, no previous studies have reported the variance explained by allergic-rhini s and GERD PRS.
We have re-wri en parts of the introduc on to reflect the missing heritability and mo vate further the molecular gene c approaches that we used in the study to inves gate the shared gene c architecture between GERD with asthma and allergic diseases as suggested by Reviewer 2 (see below).In addi on, the Reviewer will note other changes to the introduc on as a result of points 2 and 7 below and the descrip ons of GERD and atopic diseases.

2.
Further descrip on of the age of onset for these diseases would add important informa on about how these traits are comorbid.The atopic traits of focus (atopic derma s, asthma, allergic rhini s) have a trends in prevalence by age group -how does GERD fit into these trends?"GERD in pa ents with asthma between 17% and 53% depending on the size of study, study popula on-type and the asthma phenotype" .The range of 17-53% is quite large, and further interpreta on and descrip on of the popula on-type differences and the asthma phenotype difference would provide helpful background.Are there differences by age or other factors?
[Response] Thank you for this observa on.We have added some extra words to this sentence about the 17-53% comorbidity range in the introduc on to highlight why there is such a range in various studies.The sentence now reads: 'Epidemiological studies report the comorbidity of GERD in pa ents with asthma between 17% and 53% depending on the country of study (Western countries have higher prevalence of GERD), 3 study popula on-type (pa ent group/general popula on, child/adult) and the detec on methods used for asthma and GERD (symptoms alone or lab-based monitoring). 2, 4, 5' Regarding the issue of age of onset of these diseases.Asthma, eczema, allergic rhini s and GERD can affect both children and adults, with incident cases at all points in the life course.However, in recogni on that atopic diseases are more commonly a childhood disease and GERD more commonly in adulthood we have added these words to the introduc on: 'Atopic diseases are characteristically childhood diseases beginning very early in life, with 20-25% of cases continuing into adulthood as well as new onset of adult cases. 20GERD is predominantly an adult disease, although infants and adolescents can also suffer with GERD symptoms at clinically significant rates. 3' 3. Applying GenomicSEM or a similar technique to the summary sta s cs would improve the authors interpreta on of how these traits overlap gene cally, and has already shown success with correlated complex traits.Does a common factor model fit well for these traits?A exploratory factor analysis and a confirmatory factor analysis would be of interest to test if there are dis nct gene c factors. [Response] We thank reviewer's sugges on on Genomic SEM analyses.We have now performed a common factor model which fits well for most traits except for eczema, sugges ng that the common latent factor could explain the shared gene c liability to asthma, allergic rhini s and GERD.This supports our other findings.
The Abstract, Methods, Results and Discussion were accordingly updated in the main text.The addi ons are shown here including Figure 2 and Supplementary Table S10.

Genomic Structural Equation Model
Using Genomic Structural Equa on Modeling 33 (SEM) we aimed to assess if a single underlying latent factor could explain the overlap between GERD, asthma, and allergic diseases.Genomic SEM uses GWAS summary sta s cs to iden fy factor structures in the gene c correla on pa ern between traits.
Because of the conceptual and factual gene c overlap (see Figure S1) between asthma and the asthma sub-types (childhood and adult onset) we only used the general asthma trait in the common factor model.Following common prac ce, cut-off values for acceptable model fit were set at Compara ve Fit Index (CFI) > .90 and Standardized Root Mean Square Residual (SRMR) < .03.The loading of the first indicator (GERD) was fixed at 1. Asthma was a Heywood case in our model, and its variance had to be forced to be posi ve (>.001).
This could be a result of having few indicators (with one not loading on the factor at all) and should not be a threat to the interpreta on of the common factor model.

DISCUSSION
Paragraph 2: '.The Genomic SEM results also suggest that the common gene c liability to GERD, asthma and allergic rhini s can be summarised by a single underlying common factor.'Paragraph 3: .. 'neither were eczema-associated SNPs captured in the gene c variance shared between the common factors for GERD and other allergic traits from genomic SEM results.'Table S10.Results for the common factor model fit in Genomic SEM.

4.
Applying MiXeR to these summary sta s cs would also improve the depth of the analysis.The analysis could benefit from downstream evalua on and discussion of ver cal vs horizontal pleiotropy for the genes that are highlighted.
[Response] Again, we thank the reviewer's further sugges on on downstream evalua on on pleiotropy.
To provide insight into poten al ver cal pleiotropy (as well as formally test horizontal pleiotropy) we added Mendelian Randomiza on analyses to our study.Indeed, we find evidence for a causal effect of GERD on asthma and vice versa, while not observing significant horizontal pleiotropy in the MR Egger analyses.In addi on to the MR Egger test, our methods already provide a quite complete picture of horizontal pleiotropy (refer to PRS, gene c correla ons and look-up of hits in previous literature) and we deem MiXeR to fall outside of the scope of this work.
Therefore, we decided not to run MiXeR analyses at the moment.The MR analyses have now been added to the methods, results and discussion in the text.We have added them here as well:

Bidirectional two-sample Mendelian Randomization (MR)
Bi-direc onal two-sample MR analysis was performed to strengthen the causal inference of the results using TwoSample MR R package (R version 4.2.3). 34The SNPs associated with each trait at the genomewide significance level (P < 5 × 10 −8 ) with clumping window > 10,000 kb and the LD level (r 2 < 0.001) were selected as instrumental variables (IV) from published GWAS summary sta s cs (see Table 1).
The instruments' strength in the final IV set were detected with F-sta s cs a er exclusion of palindromic variants.Due to the very high sample overlap with GERD summary sta s cs, we did not use the asthma subtype summary sta s cs for MR analyses.We used the mul plica ve random effects inverse-variance weighted (IVW) model as the primary MR method to es mate the associa ons of gene cally determined each allergic trait with risk of GERD, and vice versa.Sensi vity analyses with unweighted and weighted mode-based es ma ons, weighted median, and MR-Egger methods were performed to examine the robustness of the results and iden fy horizontal pleiotropy.Leave-one-out analysis was performed to assess whether there was a significant effect on the results a er the removal of a single SNP instrument.

Bidirec onal two-sample MR analyses
There was support for a causal effect of gene c liability to asthma on increased risk of GERD, which was consistent across different sensi vity analyses (IVW OR 1.09, 95% CI 1.05-1.14,p = 6.55×10 -5 ).In the other direc on, similar effect es mates of gene c liability to GERD on increased risk of asthma were also detected (OR 1.27, 95% CI 1.12-1.43,p = 2.65× 10 −2 ).The MR-Egger regression intercepts did not significantly deviate from zero (Table S11), sugges ng no evidence of horizontal pleiotropy.
Leave-one-out and Q-heterogeneity analysis showed that the effect es mates were not overly influenced by any one variant (Figures S3 and S6).No support for associa on between other allergic traits with GERD were observed (Table S11, Figures S4-S8).

DISCUSSION
Paragraph 5: 'Furthermore, the downstream evalua on by MR results (including one pleiotropic SNP at 12q13) presented with balanced horizontal pleiotropy, meaning the poten al causal associa on between asthma and GERD did not seem to be biased by the two pleiotropic genes men oned above, but could s ll be possibly mediated by them through possible inflammatory pathways.'RESULTS: Last paragraph: 'In the general ssue expression analysis, we found evidence for a small but significant enrichment exclusively in brain ssues for GERD-associated genes; blood, spleen, lung, and small-intes ne ssues for asthma; and spleen, blood, and small intes ne ssues for eczema, sugges ng different ssues are responsible for GERD-gene and upregulated asthma-/eczema-gene signals respec vely.(Figures S18-S21)' DISCUSSION: Paragraph 6 : 'Using the MAGMA tissue enrichment analysis to detect differentially expressed gene sets for each disease we were expecting to find an overlapping tissue type for GERD and asthma or allergic rhinitis which may provide indication of a candidate gene set to explain genetic overlap.However, the results pointed to different tissue types, asthma gene sets were expressed in blood, spleen, small intestine, and as expected, in lung tissues.GERD genes were most expressed in brain tissues.Rather than shared expression in a shared tissue type it may be that shared genes for asthma and GERD behave differently in each tissue for each disease, ie that genes in blood and spleen lead to inflammatory processes causing asthma, and that in the brain they play a sensory role in reflux pain.' Minor points: 6. "a number of interven on studies aiming to improve asthma symptoms by using an -reflux (acid reducing) medica on have not been successful" Have studies tested the effec veness of using asthma medica ons to reduce GERD symptoms or in an in vitro/benchtop se ng?
[Response] As far as we are aware and a er a search there are no studies in vivo or in vitro that have looked at asthma medica ons to reduce GERD symptoms, in fact, the only reports suggest that some asthma medica ons may actually increase GERD symptoms, although as these studies are older it seems likely that this phenomenon is not reported with newer medica ons.

7.
A more detailed descrip on of the symptoms of GERD and the atopic traits (and the impact on affected pa ents quality of life) would help improve the mo va on for this study.
[Response] Thanks for this comment.We have added more words about the symptoms of GERD and each of the atopic traits to the beginning of the introduc on: 'Asthma is a common inflammatory respiratory disease causing acute dyspnoea and wheezing, affec ng 4-9% of the global child and adult popula on. 1 The most common non-allergic comorbidity of asthma is gastro-esophageal reflux disease (GERD), characterized by the reflux of gastric acid into the esophagus causing symptoms such as heartburn and regurgita on o en leading to esophagi s and complica ons such as Barre 's esophagus. 2

A 6x6 heatmap showing the gene c correla ons between all traits would be much more informa ve than what is shown in table 3.
[Response] Thanks.We have now included a 6 x6 heatmap in Figure S1 to illustrate the gene c correla on on the observa onal scale.However, we believe the informa on in Table 3 are s ll important as they include the sample v popula on prevalence, and the gene c correla ons on the liability scale considering some imbalance on the case control sample inclusion of the published GWAS.9.The y-axis label should be fixed in Figure S1 [Response] We have fixed the y-axis labels and updated the Figure S1 (now Figure S2).

Figure S10 seems to be missing data
[Response] Thank you for no cing the missing data.Indeed, FUMA could no longer provide the regional plots.
We have now replaced all the regional plots using LocusZoom.background and context for their study.In addition, the authors now present new results from the new analyses they performed.The discussion, however, is insufficient in its current form and a similar round of revisions should be performed to clarify the conclusions and take-aways from the results.As the authors point out, a primary strength of their paper stems from the triangulation of evidence from different approaches.However, as a reader I am lacking an explanation of the meaning and value of the research findings.Below I list out a few areas of the discussion that could be developed more fully: a.In Figure 1, the reported difference in predictive utility between allergic rhinitis PRS and GERD phenotype, vs GERD PRS and allergic rhinitis phenotype is interesting but isn't discussed.Synthesizing the predictive results from Figure 1 with the results from the bi-direction MR analysis would be helpful.

Please see the updated
b.The results from Table 2 (the twin models) could be discussed at greater depth.There are differing twin-model estimates across the 4 phenotypes, despite modest differences in SNP-based heritability.How does the twin model help us make more sense of these complex phenotypes?How do the results connect to the literature review in the introduction regarding disease onset and comorbidity?c.The authors suggest that the genetic enrichment of genes in the brain might be "linked to a sensory role in reflux pain."The authors may want to consider digging deeper into this finding and consider additional potential links, such as: i.There are comorbidities of internalizing psychopathology disorders, asthma, and GERD (note that asthma and anxiety have a genetic correlation of 0.406, asthma and MDD have a genetic correlation of 0.215, and asthma and PTSD have a genetic correlation of 0.458 in Table 1 of PMID: 31619474) ii.The brain has an important role in behavioral traits, such as alcohol use and smoking which both increase the risk of GERD.
iii.The brain has a key role in diet which is an important factor for GERD, and there is a genetic link to how "food-liking traits correlate with different brain areas and other food consumption traits" (PMID: 35585065).d.The three examples included above are not an exhaustive list, but they hopefully illustrate a few ways in which the discussion could be strengthened.The discussion needs revisions that emphasize the ways in which the authors' triangulation of methods and results reveals novel insights into the understanding of GERD in the context of allergic diseases.
3. For the PRS analysis, it would be helpful to understand the incremental increase in prediction accuracy ("When covariates are included in the model, then measures such as the incremental R2 [increase in R2 with the addition of the PRS to the model], which isolate the explanatory power of the PRS, should be reported."PMID: 32709988).
4. For the PRS analysis, I am concerned about the relatedness in the testing dataset (given that the samples are from a twin study).In the supplement, the authors briefly summarize that they used a "series [of] logistic regression models with clustered standard errors."I suggest the authors expand on how they handled sample relatedness when constructing these PRSs (e.g.LD structure) and when evaluating these PRSs (assessing AUC and OR).
Minor Points 1. Figure S2 should be reformatted since it has overlapping y-axis labels and cropped titles.
2. The Genomic SEM common factor could be used as a training dataset for an additional PRS to be shown in Figure 1 (as was done in Figure 3 of PMID: 30962613).This might help tie together the authors' analyses into a more unified framework.

Response to the reviewers 'Shared gene c architecture between gastro-esophageal reflux disease, asthma and allergic diseases: applica on of gene cally informa ve methods'.
Reviewer #1 (Remarks to the Author): Thank you for revising, edi ng, and rewri ng.The paper is in pre y good shape.

Reviewer #3 (Remarks to the Author):
The authors have greatly improved various parts of their study with the addi ons of key descrip ons throughout the text, a Genomic SEM common-factor model, and a bidirec onal two-sample MR analysis.Despite these improvements, I have a few major concerns that should be addressed before publica on.

[Response]
Thank you for these comments.Please see our responses below.

Major Points:
1.I am pleased to see that the authors have included Genomic SEM common-factor GWAS as a method into their analysis, as it strengthens the manuscript.However, I do have a few concerns regarding the model as it is currently presented.While the CFI = .99and SRMR = 0.04 suggest good model fit, it is peculiar that the authors have found no gene c correla ons for eczema with the other related traits (which are known to be gene cally correlated), and it is puzzling that the loading of eczema onto the common factor is zero.It appears the es mated gene c correla ons shown in the bo om row of Supplementary Figure 1 are much too low, as they are all between -0.04 and 0.02.The atopic GWAS literature has shown that eczema has a significant non-zero gene c correla on with asthma and allergic rhini s (e.g., Table 1 from PMID: 32373153 shows gene c correla ons of 0.45 for asthma and eczema, and 0.33 for hay fever and eczema; the gene c overlap between these traits has been shown in mul ple other publica ons such as PMID: 31361310 or 33436162).I am worried that the eczema summary sta s cs were not munged/incorporated into the Genomic SEM analysis properly.Given the results shown in Table 4, it seems as though all of the indicators should have posi ve loadings onto the common factor for the included traits.As the authors men oned in the manuscript, it is slightly concerning that the standardized loading for asthma on the common factor is 2.19, as standardized loadings are usually less than or equal to 1.I wonder if correc ng eczema in the model will fix the standardized loadings?It is difficult to further comment on the Genomic SEM por on of the manuscript un l this poten al bug in the analysis has been addressed.

[Response]
Thank you for the concern about the eczema GWAS sumstat munging.We have now checked the eczema GWAS summary data downloading and munging processes.The harmonized data from the GWAS Catalog (downloaded via h p:// p.ebi.ac.uk/pub/databases/gwas/summary_sta s cs/GCST90027001-GCST90028000/GCST90027161/harmonised/34454985-GCST90027161-EFO_0000274.h.tsv.gz) was originally used in our LDSC and Genomic SEM analysis, and indicated no gene c correla on between asthma and eczema or no loading.However, we observed a moderate gene c correla on when u lizing the non-harmonized summary data (downloaded via h p:// p.ebi.ac.uk/pub/databases/gwas/summary_sta s cs/GCST90027001-GCST90028000/GCST90027161/GCST90027161_buildGRCh38.tsv.gz,please see Table R1 below).
Therefore, we have chosen to use the author-uploaded non-harmonized summary data, re-run the LDSC and genomic SEM analyses and updated the results accordingly.
We have also removed some of the sentences in the Results under Genomic SEM and changed to: "All traits loaded significantly on the common factor, with the strongest loading for eczema (β=0.85,SE=0.10, p=1E-33) and the lowest loading for GERD (β=0.24,SE=0.03, p=2E-14; Figure 2, Table S10).Using the combined asthma trait instead of childhood onset and adult onset separately deteriorated fit, with SRMR falling short of the <0.10 criterion (CFI=0.96,SRMR=0.15)."

The authors have significantly improved the wri en presenta on in many parts of the manuscript.
The introduc on reads much more clearly and provides helpful background and context for their study.In addi on, the authors now present new results from the new analyses they performed.The discussion, however, is insufficient in its current form and a similar round of revisions should be performed to clarify the conclusions and take-aways from the results.As the authors point out, a primary strength of their paper stems from the triangula on of evidence from different approaches.However, as a reader I am lacking an explana on of the meaning and value of the research findings.
Below I list out a few areas of the discussion that could be developed more fully: a.In Figure 1, the reported difference in predic ve u lity between allergic rhini s PRS and GERD phenotype, vs GERD PRS and allergic rhini s phenotype is interes ng but isn't discussed.Synthesizing the predic ve results from Figure 1 with the results from the bi-direc on MR analysis would be helpful. [Response] Thank you for the opportunity to review our manuscript and provide sugges ons to improve the explana on of our research findings in the discussion.As you state, we observed GERD-PRS associated with allergic rhini s but no associa on between allergic rhini s-PRS and GERD.Furthermore, there is li le evidence for gene c correla on based on LDSC or the causal associa on between GERD and allergic rhini s based on the bi-direc onal MR analyses.Therefore, we think that the associa on of GERD-PRS and allergic rhini s could be possibly false posi ve due to the number of analyses and the lack of consistency in the direc on of effects/correla on in PRS, LDSC, and MR-analyses.
Therefore, we have revised our discussion which now reads "Allergic rhini s and GERD were weakly associated (phenotypic correla on=0.04),gene c associa on between the two was supported by the PRS analysis for GERD-PRS and allergic rhini s phenotype.However, the lack of consistency in the direc on of effects measured by the cross-twin cross trait correla ons, LDSC regression and bidirec onal MR analysis, suggests no evidence of a causal rela onship between allergic rhini s and GERD".
b.The results from Table 2 (the twin models) could be discussed at greater depth.There are differing twin-model es mates across the 4 phenotypes, despite modest differences in SNP-based heritability.
How does the twin model help us make more sense of these complex phenotypes?How do the results connect to the literature review in the introduc on regarding disease onset and comorbidity? [Response] We agree that "missing heritability" of the phenotypes based on our univariate twin models and SNPbased heritability es mates is important.However, our study focus was not to inves gate the components or explana ons of the missing heritability.Therefore, we have added the issue of missing heritability of complex traits to the limita ons of the discussion sec on, which now reads: "Finally, there may be misclassifica on of phenotypes used in current GWAS due to the need to restrict me windows to boost sample size, thus dilu ng accuracy.As a consequence, in the context of heterogeneous and highly prevalent diseases like allergic rhini s, eczema, and GERD, GWAS-iden fied common variants only explained a small part of the heritability compared to the moderate-to-high heritability found in twin studies." c.The authors suggest that the gene c enrichment of genes in the brain might be "linked to a sensory role in reflux pain."The authors may want to consider digging deeper into this finding and consider addi onal poten al links, such as: i.There are comorbidi es of internalizing psychopathology disorders, asthma, and GERD (note that asthma and anxiety have a gene c correla on of 0.406, asthma and MDD have a gene c correla on of 0.215, and asthma and PTSD have a gene c correla on of 0.458 in Table 1 of PMID: 31619474) ii.The brain has an important role in behavioral traits, such as alcohol use and smoking which both increase the risk of GERD.
iii.The brain has a key role in diet which is an important factor for GERD, and there is a gene c link to how "food-liking traits correlate with different brain areas and other food consump on traits" (PMID: 35585065).

[Response]
Thank you for great sugges ons on the poten al interpreta on based on the gene enrichment analysis.We have incorporated these references and poten al interpreta ons in the discussion which now reads "The brain is known to play an important role in behavioural traits such as smoking and food consump on; choices which are important factors for GERD development (1).Alterna vely, expressed genes may be working through other pathways such as internalizing psychopathology disorders which are known comorbidi es for both asthma (2,3) and GERD (4).Indeed, earlier work by this team and others looking at asthma and GERD comorbidity found that affec ve traits (depression, anxiety and neuro cism) were important confounders of GERD and allergic disease associa ons (5,6)."d.The three examples included above are not an exhaus ve list, but they hopefully illustrate a few ways in which the discussion could be strengthened.The discussion needs revisions that emphasize the ways in which the authors' triangula on of methods and results reveals novel insights into the understanding of GERD in the context of allergic diseases.

[Response]
We have now updated the interpreta on on asthma-GERD results as suggested above and revised the paragraph on GERD-and other allergic diseases, improving the triangula on of methods.
The discussion now reads "Allergic rhini s and GERD were weakly associated (phenotypic correla on=0.04), and a gene c associa on between GERD-PRS and allergic rhini s phenotype was supported by the PRS analysis.However, the lack of consistency in the direc on of effects measured by the cross-twin cross trait correla ons, LDSC regression and bidirec onal MR analysis, suggests no evidence of a causal rela onship between allergic rhini s and GERD.Similarly, eczema and GERD es mates were null for bidirec onal MR analyses, not suppor ng a causal connec on either.Meanwhile, the LDSC regression revealed a possible signal for gene c overlap between eczema and GERD using summary data, which we could not replicate with individual-level data." And at the end of the same paragraph: "Therefore, although the triangula on of gene c methods in our study does not support a gene c explana on for GERD-eczema and GERD-allergic rhini s comorbidity, future research harnessing larger, more accurately defined cohorts will provide further clarifica on."

3.
For the PRS analysis, it would be helpful to understand the incremental increase in predic on accuracy ("When covariates are included in the model, then measures such as the incremental R2 [increase in R2 with the addi on of the PRS to the model], which isolate the explanatory power of the PRS, should be reported."PMID: 32709988).

[Response]
We understand your sugges on and we did follow Choi et al's protocol (7) where it was possible (i.e. for the purpose of repor ng Nagelkerke R 2 and AUC for each trait as a way to "validate" the predic ng possibility in each target sample using logis c regression with clustered standard error for twin pairs, described in supplementary methods and shown in supplementary Table S7).
Addi onally, there is no true R 2 for logis c regression models (8) or generalized es ma ng equa on (GEE).Therefore, we have run the PRS analysis using logis c regression with clustered standard errors which takes into considera on the non-independence of twins and reported the pseudo R 2 and incremental pseudo R 2 (see Table R2 below).As expected, the risk es mates based on logis c regression analyses were almost iden cal to those based on GEE (see Table S8).
Therefore, considering the difficulty to interpret the pseudo R 2 sta s cs in non-linear models (9), we prefer repor ng our main PRS analysis es ma ng the popula on average effect of PRS-trait 1 on phenotypic trait 2 based on GEE models with cluster robust standard errors.However, we are open for sugges ons if the editors prefer that we also present the Table R2 below.

4.
For the PRS analysis, I am concerned about the relatedness in the tes ng dataset (given that the samples are from a twin study).In the supplement, the authors briefly summarize that they used a "series [of] logis c regression models with clustered standard errors."I suggest the authors expand on how they handled sample relatedness when construc ng these PRSs (e.g.LD structure) and when evalua ng these PRSs (assessing AUC and OR).

[Response]
Thank you for this comment.We used SBaysR to op mize the SNP-based effect sizes from the GWAS sumstats, using the pre-computed Sparse LD matrices provided by the GCTB website (see h ps://cnsgenomics.com/soware/gctb/#LDmatrices).Plink was used to calculate the raw scores for each individual.Once an individual's PRS was calculated, we assigned the same PRS for the MZ co-twins who were not directly genotyped.The reviewer is correct that PRS es mates (as well as the outcomes of interest) are indeed correlated for a twin and his/her co-twin.Therefore, when running the main crosstrait associa on analysis between PRS and phenotype, we used GEE to es mate parameters from clustered data due to twinship, i.e. the es mates of variance of the es mated coefficient were adjusted for the clustering of twins within a pair.The standard errors were es mated using robust sandwich es mators.This method has been widely used to es mate the popula on averaged effect for clustered data (10).
As a result, we have further clarified the methods in the manuscript, which now reads "Second, generalized es ma ng equa ons (GEE) with logit link func on were used to assess the associa on between PRS for each allergic disease with GERD phenotype, and the PRS for GERD with each allergic disease phenotype among all twins with available genotype data.The GEE quasi-likelihood approach modelled the correlated data by specifying an exchangeable working correla on matrix to account for the correla on due to clustering within twin pairs.Sandwich es mators correc ng for the clustering within twin pairs were applied to standard errors".

Minor Points
1. Figure S2 should be reforma ed since it has overlapping y-axis labels and cropped tles.

[Response]
Thank you.We have revised this figure.
2. The Genomic SEM common factor could be used as a training dataset for an addi onal PRS to be shown in Figure 1 (as was done in Figure 3 of PMID: 30962613).This might help e together the authors' analyses into a more unified framework.

[Response]
We agree that a PRS based on a GWAS on the common factor we iden fied using Genomic SEM would nicely connect the different parts of the paper.Given that the common factor was not part of the original plan or the focus of this paper though, we have decided to not include these extensive addi onal analyses.The expected benefit of running a common factor GWAS and deriving the PRS would be limited, because of foreseeable problems associated with extrac ng results from Genomic SEM and feeding them into another algorithm.Informa on on issues such as (control-limited) sample overlap between the traits or Heywood cases in the model will not be considered when looking only at the SNP effects on the factor, so that the resul ng GWAS can show unpredictable sta s cal ar facts, such as inflated heritability es mates or unexpected gene c correla ons with other traits.Though doable, it would be beyond the scope of the current work to carefully tackle such issues to derive a reliable PRS.

Figure 2 .
Figure 2. Common factor (F1) model for all traits as estimated in Genomic SEM.Standardized path estimates are given with their standard error.The loading of GERD was fixed to 1. Variances are indicated with circular arrows.
Figures S13-17 in the supplementary materials.

results shown in Figure S11 should be discussed in the main text [
Response]Thanks for no cing this.We have now described the results on ssue enrichment analyses and discussed the findings shown in Figures S18-S21 as shown below:

Table R2 . Associa on between GERD-PRS with allergic diseases and between allergic disease-PRS with GERD among genotyped twins using logis c regression models with clustered standard errors.
Model 2 adjusted for birth year, sex, cohort, top 5 principal components, and cohort*top 5 principal components.